In a last-ditch effort to save one of the city’s largest construction projects, developer John Rosenthal is asking Boston Mayor Martin J. Walsh’s administration for a $7.8 million tax break to help build a massive complex of buildings near Fenway Park.

Though his request was rebuffed by former mayor Thomas M. Menino, Rosenthal submitted a new application to Walsh, and so far his pitch is getting a warmer reception.

“John’s a good man and I know he’s been working on this project for a long time,” Walsh said in a recent interview with The Boston Globe. “We’re going to look at [his proposal] and do what’s best for the city.”

Rosenthal has sought tax relief for nearly a year. He said a commitment from the city would allow him to start construction later this year. Otherwise, he risks losing financing for the $500 million project.

“It’s probably do or die at this point,” he said. “And it’s also do or die for 1,800 construction jobs and the 750 permanent jobs for a shovel ready project.”

Fenway Center is one of the biggest and most complicated developments in Boston. It would create a towering complex of buildings with about 500 apartments, stores, and offices covering the ugly scar of the Massachusetts Turnpike near Kenmore Square.

Though approved by the Boston Redevelopment Authority in 2009, the project has suffered repeated delays due to a legal and permitting challenges. Its costs have risen by tens of millions of dollars.

Rosenthal is asking for $7.8 million in tax breaks over 13 years.

His tax payments to the city would steadily increase during that time, eventually reaching a total of $5.5 million a year when the project is completed. Currently, the undeveloped 4.5-acre parcel generates only $152,000 for city coffers.

Walsh has said he is open to granting tax credits for major real estate projects. But he has also vowed to overhaul the process for considering them. The mayor is reviewing the request in consultation with BRA officials.

On Wednesday, BRA spokesman Susan Elsbree said the agency has met with Rosenthal to discuss his proposal.

“We remain interested in continuing the dialogue with him, but we believe it is too early in the process to look at a specific course of action,” she said.

Fenway Center is particularly expensive and difficult to build because part of the 1.3 million-square-foot complex would straddle the turnpike. A platform to support its main parking garage and a 27-story building with 130 apartments, offices, and retail stores would cost about $35 million.

Three additional apartment buildings would be constructed on scrubby parking lots between Beacon Street and Brookline Avenue, and the state recently completed construction of a solar-powered commuter rail station off Yawkey Way.

Fenway Center is also planned to include a community center, farmers market, bike-sharing station, pedestrian and bike paths, and several stores and restaurants.

The project has won the support of neighbors and many public officials because of its potential to transform a gritty pocket of the city near Fenway Park.

But Rosenthal has struggled to lock down financing for the project. He said his building costs have risen $48 million in the last few years, throwing off the expected returns for investors. Bentall Kennedy, an international pension fund investor, has expressed interest in supporting the project.

Rosenthal said he has been able to reduce costs by $40 million through engineering efficiencies and negotiations with builders, but that he needs tax help from the city to close the remaining gap.

“At some point you can’t find more savings,” he said. “There are a lot of infrastructure costs that are unique to this development. We’ve looked everywhere, and we still have a gap.”

Bentall Kennedy did not respond to a request for comment Wednesday.

If the city grants the requested tax relief, Rosenthal said he would aim to start construction by next fall.

Shirley Leung contributed to this report. Casey Ross can be reached at cross@globe.com.